Utilization of ultrasonic measurements for the determination of various properties of a flowing material within an enclosed conduit is now a well developed art. A variety of techniques have been proposed for mounting ultrasonic transducers from the external or internal surfaces of the conduits and transmitting a generated beam through the fluid, receiving it at a second transducer, and measuring variations in transit time, (or its reciprocal which is proportional to sound speed c) or the attenuation of the signal. These ultrasonic parameters can be used to calculate flow characteristics, temperature, etc. of the fluid. Examples of such systems can be found in my prior U.S. Pat. No. 3,906,791, issued Sept. 23, 1975, and in my copending application Ser. No. 629,870, filed Nov. 7, 1975 and entitled "Ultrasonic Measuring Cell With Isolation Means" which will issue Jan. 25, 1977 as U.S. Pat. No. 4,004,461; each of which is assigned to the assignee hereof and is incorporated herein by reference.
The ultrasonic flow-sensing signal is typically emitted repeatedly or alternately from one of a pair of transducers mounted at opposite ends of a tilted diameter or diagonal across the conduit, with the direction of tilt being in the direction of flow of a material. The time delay difference (upstream time minus downstream time) between the generation of the emitted signals and their reception is a measure of the velocity of the flow. Other characteristics of the material may be determined by measurement of the attenuation of the received signal. In one embodiment a crossed pair of tilted paths are used with an emitting transducer and receiving transducer located at the ends of each of the crossed pairs. Techniques for measuring both the transit times and the attenuations are described in a number of patents and articles, some of which are listed in the above-mentioned Ser. No. 629,870.
Such previous techniques cannot provide sufficient accuracy for certain applications. The reason for the inaccuracy is that all the fluid in the pipe does not flow at the same velocity. Flow velocity at the wall is theoretically zero, while flow velocity on the pipe's axis is usually maximum. Between the wall and the axis, the velocity distribution depends on a number of factors such as Reynolds number, pipe roughness, inlet and outlet conditions, upstream conditions, vibration, temperature, density and viscosity distribution, etc. In many cases the principal factor influencing flow profile is the Reynolds number, Re. In these cases it has been the practice in the industry to multiply the meter reading by a factor K which is assumed to depend on Re alone. For an ultrasonic transmission measurement as described above, the meter factor K is defined by K = V/V.sub.d, where V.sub.d is the flow velocity measured along a tilted diameter. K typically varies from 0.750 for laminar flow (parabolic velocity distribution) to 0.93 to 0.96 for fully developed turbulent flows associated with Re = 10.sup.4 to 10.sup.7, respectively. The need for correcting V.sub.d by means of K was recognized over twenty years ago. A graph showing K vs Re was published in 1955 by Kritz, and in another form, by McShane in 1974. (J. Kritz, ISA Proc. 10 Part 2, 55-16-3, pp. 1-6 (1955); Instruments and Automation 28, 1912-1913 (Nov. 1955); J. L. McShane, pp. 897-913, in R. B. Dowdell, Ed. Flow -- Its Measurement and Control in Science and Industry, ISA (1974).) Various attempts to improve upon the accuracy afforded by an ultrasonic transmission measurement along a single tilted diameter have been proposed. These include zig-zagging a wave down the pipe (Petermann, U.S. Pat. No. 2,874,568) or using orthogonal tilted diameters (N. Suzuki, H. Nakabori and M. Yamamoto, pp. 115- 138, in C. G. Clayton, Ed., Modern Developments in Flow Measurement, Peregrinus Ltd. (1972)). These methods of multiple interrogation may provide some improvement in accuracy but they do not offer any fundamental or significant improvement because they weight the flow profile in essentially the same way as the single tilted diameter.
At the opposite extreme, ultrasonic methods have been demonstrated wherein the entire cross section of flowing fluid is weighted. In one of these methods the ultrasonic waves are transmitted axially (F. Noble, Rev. Sci. Instrum. 39(9) 1327-1331, Sept. 1968). In a second method waves are transmitted obliquely across a rectilinear duct, the waves themselves being enveloped by a square or rectangular pattern (Lynnworth, U.S. Pat. No. 3,906,791). These two methods have been practiced so far only in pipes of relatively small dimensions, and their application to large pipes would be difficult or impractical.
For large pipes the most accurate way to obtain V that has been demonstrated so far, using ultrasonic transmission methods, is the use of multiple chords, located and weighted according to mathematical formulas such as those derived by Gauss, Chebychef, or Lobatto (see U.S. Pat. No. 3,564,912, Feb. 23, 1971). This multiple chord approach provides high accuracy, but requires numerous ports to accommodate the multiple chords. Both the cost of fabrication and the risk of a leak in a pipe section, therefore, are larger than desirable.
A recent report suggests a single ultrasonic interrogation near the pipe midradius chord. (Baker and Thompson, "A Two Beam Ultrasonic Phase-Shift Flowmeter", Conf. on Fluid Flow Measurement in the Mid 1970's, Birniehill Institute, National Engineering Laboratory, East Kilbride, Glasgow, Scotland, 8-10 April 1975). That report, however, includes an experiment in air at 40kHz and a four inch diameter pipe. The resulting beam spread contributes to undesirably high levels of error (e.g. about .+-.5% total error estimated by Baker and Thompson).